Problem: Solve for $x$ and $y$ using elimination. ${3x-2y = -14}$ ${4x-3y = -22}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $3$ ${-12x+8y = 56}$ $12x-9y = -66$ Add the top and bottom equations together. $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {3x-2y = -14}\thinspace$ to find $x$ ${3x - 2}{(10)}{= -14}$ $3x-20 = -14$ $3x-20{+20} = -14{+20}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 10}$ into $\thinspace {4x-3y = -22}\thinspace$ and get the same answer for $x$ : ${4x - 3}{(10)}{= -22}$ ${x = 2}$